Comment by gmiller123456

>This seems like a very interesting question.

>After an exhaustive investigation, we found, surprisingly, that there was only one possible combination on the whole planet that would permit the eight vertices of the cube to emerge on solid land.

Not really that interesting IMHO. After enough searching your're going to find a shape that meets the criteria. If a cube had more than one configuration, they likely would have just move up a notch, and if a cube had no solution they would have moved down a notch.